Fluctuation-dissipation theorem superstatistical equilibrium distributions

III. The Fluctuation-Dissipation Theorem for the Superstatistical Equilibrium Distributions... 

In this chapter we will extend the fluctuation-dissipation theorem for general equilibrium distributions. We will consider two typical equilibrium distributions. One is the superstatistical equilibrium distribution [13]. The other is the microcanonical equilibrium distribution. 

III. THE FLUCTUATION-DISSIPATION THEOREM FOR THE SUPERSTATISTICAL EQUILIBRIUM DISTRIBUTIONS... 

A superstatistical equilibrium distribution is written as a superposition of Boltzmann distributions with different temperatures. We showed that the excess heat could be written as a superposition of correlation functions with different temperatures using the generalized fluctuation-dissipation theorem. When a relaxation time depends on a temperature, we can expect various behaviors for the area of the hysteresis loop from the fluctuation-dissipation theorem. 

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